Some elementary theorems about divisibility of 0-cycles on abelian varieties defined over finite fields.

If X is an abelian variety over a field, and L ∈ Pic(X), we know that the degree of the 0-cycle Lg is divisible by g!. As a 0-cycle, it is not, even over a field of cohomological dimension 1, but we show that over a finite field, there is some hope. [ABSTRACT FROM AUTHOR]